JAMB 1984 · UME · Q47

$XYZ$ is a triangle and $XW$ is perpendicular to $YZ$ at $W$ . If $XZ = 5$ cm, $WZ = 4$ cm and $YZ = 10$ cm, calculate $XY$ .

Worked solution (try it first)

In the right-angled triangle $XWZ$ , Pythagoras gives $XW = \sqrt{5^2 - 4^2} = \sqrt9 = 3$ cm.
$W$ lies on $YZ$ , so $YW = YZ - WZ = 10 - 4 = 6$ cm.
In the right-angled triangle $XWY$ : $XY = \sqrt{6^2 + 3^2} = \sqrt{45}$ .
Simplify: $\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt5$ cm, option B.